Problem: $ \lim_{x\to 0}(-3x^3-7x+8)=$
$-3x^3-7x+8$ defines a polynomial function. Polynomial functions are continuous across their entire domain, and their domain is all real numbers. In other words, for any polynomial $p$ and any possible input $c$, we know that this equality holds: $\lim_{x\to c}p(x)=p(c)$ Therefore, in order to find $ \lim_{x\to 0}(-3x^3-7x+8)$, we can simply evaluate $(-3x^3-7x+8)$ at $x=0$. $\begin{aligned} &\phantom{=}-3x^3-7x+8 \\\\ &=-3(0)^3-7(0)+8 \gray{\text{Substitute }x=0} \\\\ &=0-0+8 \\\\ &=8 \end{aligned}$ In conclusion, $ \lim_{x\to 0}(-3x^3-7x+8)=8$.